Rebar bond slip in diagonal tension failure of reinforced concrete beams

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1 Rbar bond lip in diagonal nion failur of rinford onr bam T. Hagaa Iniu of Tnology Simizu Corporaion Tokyo apan Rbar bond lip in diagonal nion failur of rinford onr bam T. Hagaa Iniu of Tnology Simizu Corporaion Tokyo apan Fraur Mani of Conr and Conr Sruur - Amn Durabiliy Monioring and Rrofiing of Conr Sruur- B. H. O al. (d) 200 Kora Conr Iniu Soul ISBN ABSTRACT: T influn of modling of rbar bond lip on diagonal nion failur of rinford onr bam in fini lmn analyi i xamind roug alulaion i vral modling ragi for bond lip and bond pliing fraur. T lao-plai oniuiv modl i dilaany in bond inrfa lmn rul in xniv bond pliing raking and furr propagaion of diagonal rak onnd o bond pliing rak. T parial dbonding modl bn onr and rbar bam lmn an imula diagonal nion failur mod dpnding on onfiguraion of dbonding nod. INTRODUCTION Diagonal nion failur of rinford onr ruur i inflund by many faor u a mixd mod fraur of onr loalizaion and propagaion of diagonal rak longiudinal pliing rak along nion rbar fraur bifuraion oniuiv rlaion of onr rbar bond lip and dol aion of rbar. To faor av o b akn ino aoun o imula failur manim of ruur for raional ar dign of rinford onr ruur. In prviou udi (Hagaa 2004 and Hagaa 2007a) fini lmn analyi of diagonal nion failur in a rinford onr bam a prformd uing Muli Equivaln Sri Pa Modl (MESP Modl; Hagaa 998) and failur manim r diud by analyzing numrial rul. In analyi bran-iing for fraur bifuraion influn of onr rak modl mixd mod fraur and m dpndny r foud on and xamind. Among or influning faor no xamind in prviou udi in pariular rbar bond lip and longiudinal pliing fraur ar onidrd o b qui imporan and diffiul o xamin in bo xprimnal and numrial invigaion. T bond lip of rinforing bar i onidrd o influn failur roug manim a bond lip inra id of diagonal rak and ang propagaion of rak o unabl propagaion. T bond lip alo au pliing rak of onr ovr along rinforing bar a onn i diagonal rak and i rul in a riggr of diagonal nion ollap of bam in an unabl mannr. In i udy (Hagaa 2007b 2008 and 2009) influn of modling of rbar bond lip on diagonal nion failur of rinford onr bam in fini lmn analyi i xamind roug alulaion i vral modling ragi for bond lip and bond pliing fraur. 2 BOND STRESS-SLIP MODELS Rbar bond lip i uually imulad by uing inrfa lmn i a bond r - lip S rlaionip u a Eq. (Wi & Kikra 2007) in fini lmn analyi of rinford onr ruur. Hovr bond r-lip rlaionip obaind from pullou xprimn of rinford onr ar knon o b no uniqu bu rongly dpnd on boundary ondiion in xprimn u a mbddd lng of rbar dian of maurmn poiion L/2=600mm L=20mm L=20mm Figur. Exprimnal raking parn of BN50 afr failur. Tabl. Modl for bond r-lip rlaionip. Modl Lng L of Loaion pullou pimn (mm) 2x L - S or S quaion b- Non Non Eq b Eq b Eq b quarr iffn 4.8 of modl b-3 b Eq Bond rng ( Nmm 2 )

2 = D ( T ) T proporionaliy offiin D(T) moiur prmabiliy and i i a nonlina of rlaiv umidiy and mpraur & Najjar 972). T moiur ma balan a variaion in im of ar ma volum of onr (ar onn ) b q divrgn of moiur flux = T ar onn an b xprd a of vaporabl ar (apillary a vapor and adorbd ar) and non- (mially bound) ar n (Mil Panazopoulo & Mill 995). I i ra aum a vaporabl ar i a fu rlaiv umidiy dgr of ydraion dgr of ilia fum raion α i.. = = ag-dpndn orpion/dorpion (Norling Mjonll 997). Undr i aum by ubiuing Equaion ino Equai obain + ( D ) = α& + α& + r / i lop of orpion/ iorm (alo alld moiur apa govrning quaion (Equaion 3) mu b by appropria boundary and iniial ondii T rlaion bn amoun of ar and rlaiv umidiy i alld iorm if maurd i inraing umidiy and dorpion iorm in a. Ngling ir diffrn (Xi al. folloing orpion iorm ill b rfrn o bo orpion and dorpion By ay if yri of iorm ould b akn ino aoun o rlaion vaporabl ar v rlaiv umi b ud aording o ign of varia rlaiviy umidiy. T ap of iorm for HPC i inflund by many p pially o a influn xn and mial raion and in urn drm ruur and por iz diribuion (arraio mn mial ompoiion SF uring im and mod mpraur mix.). In liraur variou formulaio found o drib orpion iorm onr (Xi al. 994). Hovr in papr mi-mpirial xprion pro Norling Mjornll (997) i adopd b Proding of FraMCoS-7 May

3 = D ( T ) () T proporionaliy offiin D(T) i alld moiur prmabiliy and i i a nonlinar funion of rlaiv umidiy and mpraur T (Bažan & Najjar 972). T moiur ma balan rquir a variaion in im of ar ma pr uni volum of onr (ar onn ) b qual o divrgn of moiur flux ( α α ) = G (α α ) 0 0 (2) T ar onn an b xprd a um of vaporabl ar (apillary ar ar vapor and adorbd ar) and non-vaporabl (mially bound) ar n (Mill 966 Panazopoulo & Mill 995). I i raonabl o aum a vaporabl ar i a funion of rlaiv umidiy dgr of ydraion α and dgr of ilia fum raion α i.. =(αα) = ag-dpndn orpion/dorpion iorm (Norling Mjonll 997). Undr i aumpion and by ubiuing Equaion ino Equaion 2 on obain + ( D ) = α& + α& + &n (3) r / i lop of orpion/dorpion iorm (alo alld moiur apaiy). T govrning quaion (Equaion 3) mu b ompld by appropria boundary and iniial ondiion. T rlaion bn amoun of vaporabl ar and rlaiv umidiy i alld adorpion iorm if maurd i inraing rlaiviy umidiy and dorpion iorm in oppoi a. Ngling ir diffrn (Xi al. 994) in folloing orpion iorm ill b ud i rfrn o bo orpion and dorpion ondiion. By ay if yri of moiur iorm ould b akn ino aoun o diffrn rlaion vaporabl ar v rlaiv umidiy mu b ud aording o ign of variaion of rlaiviy umidiy. T ap of orpion iorm for HPC i inflund by many paramr pially o a influn xn and ra of mial raion and in urn drmin por ruur and por iz diribuion (ar-o-mn raio mn mial ompoiion SF onn uring im and mod mpraur mix addiiv.). In liraur variou formulaion an b found o drib orpion iorm of normal onr (Xi al. 994). Hovr in prn papr mi-mpirial xprion propod by Norling Mjornll (997) i adopd bau i Proding of FraMCoS-7 May α ) α ) K (α α ) = xpliily aoun for voluion of ydraion raion and SF onn. Ti orpion iorm rad + (4) r fir rm (gl iorm) rprn pyially bound (adorbd) ar and ond rm (apillary iorm) rprn apillary ar. Ti xprion i valid only for lo onn of SF. T offiin G rprn amoun of ar pr uni volum ld in gl por a 00% rlaiv umidiy and i an b xprd (Norling Mjornll 997) a α + k α G (α α ) = k vg vg (5) r kvg and kvg ar marial paramr. From maximum amoun of ar pr uni volum a an fill all por (bo apillary por and gl por) on an alula K a on obain 0 K (α α ) = α α G g α α g α α (6) T marial paramr kvg and kvg and g an b alibrad by fiing xprimnal daa rlvan o fr (vaporabl) ar onn in onr a variou ag (Di Luzio & Cuai 2009b). 2.2 Tmpraur voluion No a a arly ag in mial raion aoiad i mn ydraion and SF raion ar xormi mpraur fild i no uniform for non-adiabai ym vn if nvironmnal mpraur i onan. Ha onduion an b dribd in onr a la for mpraur no xding 00 C (Bažan & Kaplan 996) by Fourir la i rad q = λ T (7) r q i a flux T i abolu mpraur and λ i a onduiviy; in i

4 = D ( T ) T proporionaliy offiin D(T) moiur prmabiliy and i i a nonlina of rlaiv umidiy and mpraur & Najjar 972). T moiur ma balan a variaion in im of ar ma volum of onr (ar onn ) b q divrgn of moiur flux = T ar onn an b xprd a of vaporabl ar (apillary a vapor and adorbd ar) and non- (mially bound) ar n (Mil Panazopoulo & Mill 995). I i ra aum a vaporabl ar i a fu rlaiv umidiy dgr of ydraion dgr of ilia fum raion α i.. = = ag-dpndn orpion/dorpion (Norling Mjonll 997). Undr i aum by ubiuing Equaion ino Equai obain + ( D ) = α& + α& + r / i lop of orpion/ iorm (alo alld moiur apa govrning quaion (Equaion 3) mu b by appropria boundary and iniial ondii T rlaion bn amoun of ar and rlaiv umidiy i alld iorm if maurd i inraing umidiy and dorpion iorm in a. Ngling ir diffrn (Xi al. folloing orpion iorm ill b rfrn o bo orpion and dorpion By ay if yri of iorm ould b akn ino aoun o rlaion vaporabl ar v rlaiv umi b ud aording o ign of varia rlaiviy umidiy. T ap of iorm for HPC i inflund by many p pially o a influn xn and mial raion and in urn drm ruur and por iz diribuion (arraio mn mial ompoiion SF uring im and mod mpraur mix.). In liraur variou formulaio found o drib orpion iorm onr (Xi al. 994). Hovr in papr mi-mpirial xprion pro Norling Mjornll (997) i adopd b Proding of FraMCoS-7 May

5 = D ( T ) () T proporionaliy offiin D(T) i alld moiur prmabiliy and i i a nonlinar funion of rlaiv umidiy and mpraur T (Bažan & Najjar 972). T moiur ma balan rquir a variaion in im of ar ma pr uni volum of onr (ar onn ) b qual o divrgn of moiur flux ( α α ) = G (α α ) 0 0 (2) T ar onn an b xprd a um of vaporabl ar (apillary ar ar vapor and adorbd ar) and non-vaporabl (mially bound) ar n (Mill 966 Panazopoulo & Mill 995). I i raonabl o aum a vaporabl ar i a funion of rlaiv umidiy dgr of ydraion α and dgr of ilia fum raion α i.. =(αα) = ag-dpndn orpion/dorpion iorm (Norling Mjonll 997). Undr i aumpion and by ubiuing Equaion ino Equaion 2 on obain + ( D ) = α& + α& + &n (3) r / i lop of orpion/dorpion iorm (alo alld moiur apaiy). T govrning quaion (Equaion 3) mu b ompld by appropria boundary and iniial ondiion. T rlaion bn amoun of vaporabl ar and rlaiv umidiy i alld adorpion iorm if maurd i inraing rlaiviy umidiy and dorpion iorm in oppoi a. Ngling ir diffrn (Xi al. 994) in folloing orpion iorm ill b ud i rfrn o bo orpion and dorpion ondiion. By ay if yri of moiur iorm ould b akn ino aoun o diffrn rlaion vaporabl ar v rlaiv umidiy mu b ud aording o ign of variaion of rlaiviy umidiy. T ap of orpion iorm for HPC i inflund by many paramr pially o a influn xn and ra of mial raion and in urn drmin por ruur and por iz diribuion (ar-o-mn raio mn mial ompoiion SF onn uring im and mod mpraur mix addiiv.). In liraur variou formulaion an b found o drib orpion iorm of normal onr (Xi al. 994). Hovr in prn papr mi-mpirial xprion propod by Norling Mjornll (997) i adopd bau i Proding of FraMCoS-7 May α ) α ) K (α α ) = xpliily aoun for voluion of ydraion raion and SF onn. Ti orpion iorm rad + (4) r fir rm (gl iorm) rprn pyially bound (adorbd) ar and ond rm (apillary iorm) rprn apillary ar. Ti xprion i valid only for lo onn of SF. T offiin G rprn amoun of ar pr uni volum ld in gl por a 00% rlaiv umidiy and i an b xprd (Norling Mjornll 997) a α + k α G (α α ) = k vg vg (5) r kvg and kvg ar marial paramr. From maximum amoun of ar pr uni volum a an fill all por (bo apillary por and gl por) on an alula K a on obain 0 K (α α ) = α α G g α α g α α (6) T marial paramr kvg and kvg and g an b alibrad by fiing xprimnal daa rlvan o fr (vaporabl) ar onn in onr a variou ag (Di Luzio & Cuai 2009b). 2.2 Tmpraur voluion No a a arly ag in mial raion aoiad i mn ydraion and SF raion ar xormi mpraur fild i no uniform for non-adiabai ym vn if nvironmnal mpraur i onan. Ha onduion an b dribd in onr a la for mpraur no xding 00 C (Bažan & Kaplan 996) by Fourir la i rad q = λ T (7) r q i a flux T i abolu mpraur and λ i a onduiviy; in i

6 = D ( T ) T proporionaliy offiin D(T) moiur prmabiliy and i i a nonlina of rlaiv umidiy and mpraur & Najjar 972). T moiur ma balan a variaion in im of ar ma volum of onr (ar onn ) b q divrgn of moiur flux = T ar onn an b xprd a of vaporabl ar (apillary a vapor and adorbd ar) and non- (mially bound) ar n (Mil Panazopoulo & Mill 995). I i ra aum a vaporabl ar i a fu rlaiv umidiy dgr of ydraion dgr of ilia fum raion α i.. = = ag-dpndn orpion/dorpion (Norling Mjonll 997). Undr i aum by ubiuing Equaion ino Equai obain + ( D ) = α& + α& + r / i lop of orpion/ iorm (alo alld moiur apa govrning quaion (Equaion 3) mu b by appropria boundary and iniial ondii T rlaion bn amoun of ar and rlaiv umidiy i alld iorm if maurd i inraing umidiy and dorpion iorm in a. Ngling ir diffrn (Xi al. folloing orpion iorm ill b rfrn o bo orpion and dorpion By ay if yri of iorm ould b akn ino aoun o rlaion vaporabl ar v rlaiv umi b ud aording o ign of varia rlaiviy umidiy. T ap of iorm for HPC i inflund by many p pially o a influn xn and mial raion and in urn drm ruur and por iz diribuion (arraio mn mial ompoiion SF uring im and mod mpraur mix.). In liraur variou formulaio found o drib orpion iorm onr (Xi al. 994). Hovr in papr mi-mpirial xprion pro Norling Mjornll (997) i adopd b Proding of FraMCoS-7 May

7 = D ( T ) () T proporionaliy offiin D(T) i alld moiur prmabiliy and i i a nonlinar funion of rlaiv umidiy and mpraur T (Bažan & Najjar 972). T moiur ma balan rquir a variaion in im of ar ma pr uni volum of onr (ar onn ) b qual o divrgn of moiur flux ( α α ) = G (α α ) 0 0 (2) T ar onn an b xprd a um of vaporabl ar (apillary ar ar vapor and adorbd ar) and non-vaporabl (mially bound) ar n (Mill 966 Panazopoulo & Mill 995). I i raonabl o aum a vaporabl ar i a funion of rlaiv umidiy dgr of ydraion α and dgr of ilia fum raion α i.. =(αα) = ag-dpndn orpion/dorpion iorm (Norling Mjonll 997). Undr i aumpion and by ubiuing Equaion ino Equaion 2 on obain + ( D ) = α& + α& + &n (3) r / i lop of orpion/dorpion iorm (alo alld moiur apaiy). T govrning quaion (Equaion 3) mu b ompld by appropria boundary and iniial ondiion. T rlaion bn amoun of vaporabl ar and rlaiv umidiy i alld adorpion iorm if maurd i inraing rlaiviy umidiy and dorpion iorm in oppoi a. Ngling ir diffrn (Xi al. 994) in folloing orpion iorm ill b ud i rfrn o bo orpion and dorpion ondiion. By ay if yri of moiur iorm ould b akn ino aoun o diffrn rlaion vaporabl ar v rlaiv umidiy mu b ud aording o ign of variaion of rlaiviy umidiy. T ap of orpion iorm for HPC i inflund by many paramr pially o a influn xn and ra of mial raion and in urn drmin por ruur and por iz diribuion (ar-o-mn raio mn mial ompoiion SF onn uring im and mod mpraur mix addiiv.). In liraur variou formulaion an b found o drib orpion iorm of normal onr (Xi al. 994). Hovr in prn papr mi-mpirial xprion propod by Norling Mjornll (997) i adopd bau i Proding of FraMCoS-7 May α ) α ) K (α α ) = xpliily aoun for voluion of ydraion raion and SF onn. Ti orpion iorm rad + (4) r fir rm (gl iorm) rprn pyially bound (adorbd) ar and ond rm (apillary iorm) rprn apillary ar. Ti xprion i valid only for lo onn of SF. T offiin G rprn amoun of ar pr uni volum ld in gl por a 00% rlaiv umidiy and i an b xprd (Norling Mjornll 997) a α + k α G (α α ) = k vg vg (5) r kvg and kvg ar marial paramr. From maximum amoun of ar pr uni volum a an fill all por (bo apillary por and gl por) on an alula K a on obain 0 K (α α ) = α α G g α α g α α (6) T marial paramr kvg and kvg and g an b alibrad by fiing xprimnal daa rlvan o fr (vaporabl) ar onn in onr a variou ag (Di Luzio & Cuai 2009b). 2.2 Tmpraur voluion No a a arly ag in mial raion aoiad i mn ydraion and SF raion ar xormi mpraur fild i no uniform for non-adiabai ym vn if nvironmnal mpraur i onan. Ha onduion an b dribd in onr a la for mpraur no xding 00 C (Bažan & Kaplan 996) by Fourir la i rad q = λ T (7) r q i a flux T i abolu mpraur and λ i a onduiviy; in i

8 = D ( T ) T proporionaliy offiin D(T) moiur prmabiliy and i i a nonlina of rlaiv umidiy and mpraur & Najjar 972). T moiur ma balan a variaion in im of ar ma volum of onr (ar onn ) b q divrgn of moiur flux = T ar onn an b xprd a of vaporabl ar (apillary a vapor and adorbd ar) and non- (mially bound) ar n (Mil Panazopoulo & Mill 995). I i ra aum a vaporabl ar i a fu rlaiv umidiy dgr of ydraion dgr of ilia fum raion α i.. = = ag-dpndn orpion/dorpion (Norling Mjonll 997). Undr i aum by ubiuing Equaion ino Equai obain + ( D ) = α& + α& + r / i lop of orpion/ iorm (alo alld moiur apa govrning quaion (Equaion 3) mu b by appropria boundary and iniial ondii T rlaion bn amoun of ar and rlaiv umidiy i alld iorm if maurd i inraing umidiy and dorpion iorm in a. Ngling ir diffrn (Xi al. folloing orpion iorm ill b rfrn o bo orpion and dorpion By ay if yri of iorm ould b akn ino aoun o rlaion vaporabl ar v rlaiv umi b ud aording o ign of varia rlaiviy umidiy. T ap of iorm for HPC i inflund by many p pially o a influn xn and mial raion and in urn drm ruur and por iz diribuion (arraio mn mial ompoiion SF uring im and mod mpraur mix.). In liraur variou formulaio found o drib orpion iorm onr (Xi al. 994). Hovr in papr mi-mpirial xprion pro Norling Mjornll (997) i adopd b Proding of FraMCoS-7 May